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Simplifying (2k + 7) * x + 3y + 1 = 0 Reorder the terms: (7 + 2k) * x + 3y + 1 = 0 Reorder the terms for easier multiplication: x(7 + 2k) + 3y + 1 = 0 (7 * x + 2k * x) + 3y + 1 = 0 Reorder the terms: (2kx + 7x) + 3y + 1 = 0 (2kx + 7x) + 3y + 1 = 0 Reorder the terms: 1 + 2kx + 7x + 3y = 0 Solving 1 + 2kx + 7x + 3y = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2kx + 7x + -1 + 3y = 0 + -1 Reorder the terms: 1 + -1 + 2kx + 7x + 3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2kx + 7x + 3y = 0 + -1 2kx + 7x + 3y = 0 + -1 Combine like terms: 0 + -1 = -1 2kx + 7x + 3y = -1 Add '-7x' to each side of the equation. 2kx + 7x + -7x + 3y = -1 + -7x Combine like terms: 7x + -7x = 0 2kx + 0 + 3y = -1 + -7x 2kx + 3y = -1 + -7x Add '-3y' to each side of the equation. 2kx + 3y + -3y = -1 + -7x + -3y Combine like terms: 3y + -3y = 0 2kx + 0 = -1 + -7x + -3y 2kx = -1 + -7x + -3y Divide each side by '2x'. k = -0.5x-1 + -3.5 + -1.5x-1y Simplifying k = -0.5x-1 + -3.5 + -1.5x-1y Reorder the terms: k = -3.5 + -0.5x-1 + -1.5x-1y
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